# Scoring

There are 3 major components of the Trial Score.

1. Cost Factor: How much does the system (sensors) cost?

2. Efficiency Factor: How fast or efficiently did the system complete the task(s)

## Cost Factor

The Cost Factor $$CF$$ compares the cost of the sensors chosen by the team to the average of all sensor configurations across all teams.

• $$TC$$ is the total cost of the sensors in the team’s configuration.

• $$TC_{avg}$$ is the average sensor cost across all teams.

• $$w_c$$ is a weighting constant for cost factor.

Cost Factor

$CF = w_c \cdot \frac{TC_{avg}}{TC}$

## Efficiency Factor

The Efficiency Factor $$EF_i$$ for order $$i$$ compares the time to complete order $$i$$ for the team to the average of all teams’s times to complete order $$i$$.

• $$T_i$$ is the time to complete order $$i$$

• $$T_{avg_{i}}$$ is the average time to complete order $$i$$ for all teams

• $$w_t$$ is a weighting constant for efficiency factor.

Efficiency Factor

$EF_i = w_t \cdot \frac{T_{avg_{i}}}{T_i}$

Each submitted order will recieve a task score based on the required task for that order (Kitting, Assembly, or Combined). Each task score is generated from Boolean conditions.

• A kitting task has $$n$$ parts that need to be placed on the kitting tray.

• A shipment has $$m$$ parts on the kitting tray.

• For each task there are two Boolean conditions:

• $$\texttt{isCorrectTrayID} \rightarrow A ~~$$ : true if the shipment tray ID is correct.

• $$\texttt{isCorrectDestination} \rightarrow B ~~$$ : true if the shipment was sent to the correct destination.

• For each quadrant $$q$$ of the kitting tray there are four Boolean conditions:

• $$\texttt{isCorrectType}_{q} \rightarrow C ~~$$ : true if the part type in quadrant $$q$$ is correct.

• $$\texttt{isCorrectColor}_{q} \rightarrow D ~~$$ : true if the part color in quadrant $$q$$ is correct.

• $$\texttt{isFlipped}_{q} \rightarrow E ~~$$ : true if the part in quadrant $$q$$ is flipped.

• $$\texttt{isFaulty}_{q} \rightarrow F ~~$$ : true if the part in quadrant $$q$$ is faulty.

Tray Points

$\begin{split}\texttt{pt}_{t} = \begin{cases} 1, &\text{if} ~~ A \\ 0, &\text{otherwise} \\ \end{cases}\end{split}$

$\begin{split}\texttt{pt}_q = \begin{cases} 0, &\text{if} ~~ \lnot C \lor E \lor F \\ 3, &\text{if} ~~ D \\ 2, &\text{if} ~~ \lnot D \\ \end{cases}\end{split}$

Bonus Points

$\begin{split}\texttt{pt}_b = \begin{cases} n, &\text{if} ~~ \sum_{q}^{n}{\texttt{pt}_q} = n\times 3 \\ 0, &\text{otherwise} \\ \end{cases}\end{split}$

Extra Parts Penalty

A penalty is only applied if more parts are on the tray than needed.

$\begin{split}\texttt{pn}_{ep} = \begin{cases} m - n, &\text{if} ~~ m>n \\ 0, &\text{otherwise} \\ \end{cases}\end{split}$

Wrong Tray Penalty

$\begin{split}\texttt{pn}_{t} = \begin{cases} 1, &\text{if} ~~ \lnot A \\ 0, &\text{otherwise} \\ \end{cases}\end{split}$

Destination Multiplier

$\begin{split}\texttt{pm}_{d} = \begin{cases} 1, &\text{if}\, B \\ 0, &\text{otherwise} \\ \end{cases}\end{split}$

$S_{k} = (\texttt{pt}_{t} + \sum_{q}^{n}{(\texttt{pt}_q)} + \texttt{pt}_b - \texttt{pn}_{ep} - \texttt{pn}_{t}) \times \texttt{pm}_{d}$

The task score cannot be negative, if the calculation is negative the score will be set as 0.

• An assembly task has $$n$$ parts that need to be assembled into the insert.

• For each task there is one Boolean condition:

• $$\texttt{isCorrectStation} \rightarrow A ~~$$ : true if the assembly was done at the correct station (as1, as2, as3, or as4).

• Each slot $$s$$ in the insert has the following Boolean conditions:

• $$\texttt{isAssembled}_{s} \rightarrow B ~~$$ : true if the part in slot $$s$$ is reported as assembled.

• $$\texttt{isCorrectColor}_{s} \rightarrow C ~~$$ : true if the part in slot $$s$$ is of correct color.

• $$\texttt{isCorrectPose}_{s} \rightarrow D ~~$$ : true if the part in slot $$s$$ has the correct pose.

Slot Points

$\begin{split}\texttt{pt}_s = \begin{cases} 0, &\text{if} ~~ \lnot B \\ 3, &\text{if} ~~ C \land D \\ 2, &\text{if} ~~ C \lor D \\ 1, &\text{if} ~~ \lnot C \land \lnot D\\ \end{cases}\end{split}$

Bonus Points

$\begin{split}\texttt{pt}_b = \begin{cases} n, &\text{if} ~~ \sum_{s}^{n}{\texttt{pt}_{s}} = n\times 3 \\ 0, &\text{otherwise} \\ \end{cases}\end{split}$

Station Multiplier

$\begin{split}\texttt{pm}_{s} = \begin{cases} 1, &\text{if}\, A \\ 0, &\text{otherwise} \\ \end{cases}\end{split}$

$S_{a} = (\sum_{s}^{n}{\texttt{pt}_s} + \texttt{pt}_b) \times \texttt{pm}_{s}$

• A combined task has $$n$$ parts that need to be gathered from the environment and assembled to the insert.

• For each task there is one Boolean condition:

• $$\texttt{isCorrectStation} \rightarrow A ~~$$ : true if the assembly was done at the correct station (as1, as2, as3, or as4).

• Each slot $$s$$ in the insert has the following Boolean conditions:

• $$\texttt{isAssembled}_{s} \rightarrow B ~~$$ : true if the part in slot $$s$$ is reported as assembled.

• $$\texttt{isCorrectColor}_{s} \rightarrow C ~~$$ : true if the part in slot $$s$$ is of correct color.

• $$\texttt{isCorrectPose}_{s} \rightarrow D ~~$$ : true if the part in slot $$s$$ has the correct pose.

Slot Points

$\begin{split}\texttt{pt}_s = \begin{cases} 0, &\text{if} ~~ \lnot B \\ 5, &\text{if} ~~ C \land D \\ 4, &\text{if} ~~ C \lor D \\ 3, &\text{if} ~~ \lnot C \land \lnot D\\ \end{cases}\end{split}$

Bonus Points

$\begin{split}\texttt{pt}_b = \begin{cases} n, &\text{if} ~~ \sum_{s}^{n}{\texttt{pt}_{s}} = n\times 5 \\ 0, &\text{otherwise} \\ \end{cases}\end{split}$

Station Multiplier

$\begin{split}\texttt{pm}_{s} = \begin{cases} 1, &\text{if}\, A \\ 0, &\text{otherwise} \\ \end{cases}\end{split}$

$S_{c} = (\sum_{s}^{n}{\texttt{pt}_s} + \texttt{pt}_b) \times \texttt{pm}_{s}$

## Trial Score

The trial score $$TS$$ combines the cost factor, efficiency factors and task scores into a single score for ranking the teams.

• For each order there is one Boolean condition:

• $$\texttt{isPriorityOrder} \rightarrow A ~~$$ : true if the order is classified as a priority order

Priority Multiplier

$\begin{split}\texttt{pm}_p = \begin{cases} 3, &\text{if} ~~ A \\ 1, &\text{otherwise} \\ \end{cases}\end{split}$

Trial Score

$TS = CF \times \sum_{i=0}^{n}{(\texttt{pm}_p \times EF_i \times S_i)}$